Air Traffic Control directs the aircraft from the holding stacks (Bovingdon, Lambourne, Ockham, Biggin) onto the ILS localiser for the relevant runway.
If you look at the "Initial Approach Procedures (Without Radar Control) to ILS RWY 27L/R" documents on the AIS site you get a very rough idea of the paths aircraft will follow.
However the actual paths can vary considerably; different aircraft need different speeds and spacing from the aircraft in front, so the exact point at which they turn and join varies according to directions from ATC.
Be glad you're not on a takeoff path too! I'm under an approach and takeoff path.. can get noisy (not that I mind)